# What values of Avogadro's Number did Jean Perrin come up with?

I am currently plundering the contents of the $$1969$$ reprint of the 2nd edition of Data and Formulae for Engineering Students published by Pergamon International (authors J.C. Anderson, D.M. Hum, B.G. Neal, J.H. Whitelaw) which I found in my bookshelf.

In chapter 3: Physical Constants, it states:

Avogadro's number $$\qquad \text N \qquad = 6.023 \times 10^{26} \ / \text {kg mole}$$

It is understood that the definition of Avogadro's number (henceforth here $$N_0$$) was rationalised in 1971 to be the amount of substance that contains as many elementary entities as there are atoms in $$12$$ grams of carbon-$$12$$, but it is unclear (from the sources I have managed to find) what that number actually was, merely that it was known to be approximately $$6.02 \times 10^{23}$$.

It is also understood that the current definition of $$N_0$$ (as exactly $$6.02214076 \times 10^{23}$$) happened in 2019.

I am interested to know where the $$6.023$$ might have come from in the above book, or whether it's a mistake brought about by a conflation of the 2nd and 3rd decimal places (23) with the exponent of $$10$$. It is remarkably tempting to remember the $$23$$-ness of Avogadro's number and accidentally apply it to the mantissa.

The question is: what values of $$N_0$$ were in circulation before the 2019 redefinition? In particular, what value of $$N_0$$ was determined by Jean Perrin (who actually did most of the initial hard work of measuring it)?

It occurs to me that if it "suddenly" changed from $$6.023$$ to $$6.022...$$, that's a (relatively) large change to standards which in general are known to an accuracy of well under parts per million. That is to my mind something of a discrepancy.

• In an older publication from behind the Iron Curtain I see two values for Avogadro's number: $N_{\mathrm{A}}^{\mathrm{Ph}} = (6.02252 \pm 0.00016) \cdot 10^{26} \mathrm{kmol}^{-1}$ and $N_{\mathrm{A}}^{\mathrm{Ch}} = (6.02336 \pm 0.00020) \cdot 10^{26} \mathrm{kmol}^{-1}$, where "Ph" presumably stands for physics and "Ch" stands for chemistry? Jul 20 at 10:44
• Perrin only contributed three of the thirteen different values (each determined by a different method) listed in his seminal publication. His values were based on measurements of Brownian motion: $(70.5, 71.5, 65) \cdot 10^{22}$. Jean Perrin, "Mouvement brownien et réalité moléculaire." Annales de chimie et de physique, 8th Series, Vol. 18, Sep. 1909, pp. 5-113 (scan at BnF Gallica) Jul 20 at 11:25
• @njuffa sorry, thought that was clear: although it was "called" Avogadro's Number in the text, it was not A.N. that they actually did describe, but the number of particles in a kilogram-mole, which is 1000x the number in a mole, which is A.N. Jul 20 at 11:27
• @njuffa ... and that value of $N_A = 6.225 \times 10^{23}$, I sincerely hope it was $N_A = 6.0225 \times 10^{23}$ or there's a serious mistake in that book. Jul 20 at 11:29
• @njuffa The kilogram-mole $\text {kg mol}$ is the number of C12 atoms in 12 kg of C12, like the gram-mole is the number of C12 atoms in 12 g of C12. The latter is "almost" the same thing as a "mole", which is Avogadro's number of things. A "gram-mole" (which is what a "mole" was before 2019) is very close to a mole, but the old term "gram-mole" is used to refer specifically to the pre-2019 definition. Similarly a kilomole is "almost" the same as a kilogram-mole. Jul 20 at 11:57

My 1975-76 CRC Handbook (56th edition) states:

Avogadro's number. -- The number of molecules in one mole or gram-molecular weight of a substance. A number of values of the Avogadro number, which is usually denoted by $$N_{A}$$, have been found by various methods, generally lying within a range of 1% about the value of $$6.02252 \times 10^{23}$$ per gram mole.

Rounding could easily make it $$6.023 \times 10^{23}$$ which is still within the 1% range given.